Pressure change with constant volume

1. Nov 23, 2013

1. The problem statement, all variables and given/known data
Given two moles of some gas with two atoms per molecule which has energy $U=aK_{B}T$.
Assume the initial pressure is $P_{i}= 2$ Atm and the initial volume is $P_{i}= 0.001\ m^{3}$.
Now we heat it in an isochoric process to $2P_{i}$.

What would be $\Delta T$?
What would be the work required to do that?
What would be the change in the gas particles' internal energy?

2. Relevant equations
$U=aK_{B}T$
$dU=PdS-TdV$

3. The attempt at a solution
Well using the first law of thermodynamics, I got that under constant volume $dV=0$ so $\frac{dQ}{dT}=\frac{\partial U}{\partial T}$ so the entire energy that we spent on heating would be transferred into the gas.
What's a tricky to me is to formulate the change in temperature as a function of pressure because $dV=0$ so I'd really welcome a hint.

Thanks!

Last edited: Nov 23, 2013
2. Nov 23, 2013

TSny

Oops, check that.

Can you assume the gas obeys the ideal gas law?

3. Nov 24, 2013

And yes of course it was a typo :) it's supposed to be $dU=TdS-PdV$